“The thought-provoking and very interesting proposal of this book amounts to claiming that one can realize the dream (starting at least from the Leibnitian Calculemus) of generating all possible purely logical propositions by means of a mechanical computation. Otherwise stated, and carefully pointed out in this book as well, a full mechanization of logic is possible by renouncing the idea of starting from a set of purely logical axioms. This of course does not mean that a suitable axiomless version, axiomless predicate calculus (APC) of full first-order, becomes ipso facto a decidable system. Rather, a suitable decidable subsystem of APC is carefully built up in detail chiefly in order to show both its own efficiency and its relevance from a logical and philosophical point of view. A really relevant achievement.”

The book aims at building a mechanical way to do inferences by making use of arithmetic operations (addition, product, subtraction, division) on a string of numbers representing statements. In this way logic is reduced to a branch of the combinatory calculus. It covers the field of traditional logic by showing that any kind of inference can be mechanically reduced to three-variables and two-premise inferences. Meriological inferences can also be easily treated in this way. Possible applications of the field would be in artificial intelligence, classical computation, and quantum computation. The book covers the following subjects: structural description of space; three-variable inferences through products, sums, subtractions, and divisions; generalization to n variables; relations; and applications.